publication . Article . Preprint . 1999

Rational dynamical zeta functions for birational transformations

Abarenkova, N.; ANGLÈS d'AURIAC, J.-Ch.; Boukraa, S.; Hassani, S.; Maillard, J.-M.;
Open Access
  • Published: 01 Feb 1999 Journal: Physica A: Statistical Mechanics and its Applications, volume 264, pages 264-293 (issn: 0378-4371, Copyright policy)
  • Publisher: Elsevier BV
  • Country: France
Abstract
We propose a conjecture for the exact expression of the dynamical zeta function for a family of birational transformations of two variables, depending on two parameters. This conjectured function is a simple rational expression with integer coefficients. This yields an algebraic value for the topological entropy. Furthermore the generating function for the Arnold complexity is also conjectured to be a rational expression with integer coefficients with the same singularities as for the dynamical zeta function. This leads, at least in this example, to an equality between the Arnold complexity and the exponential of the topological entropy. We also give a semi-nume...
Subjects
free text keywords: Statistics and Probability, Condensed Matter Physics, Generating function, Integer, Conjecture, Riemann zeta function, symbols.namesake, symbols, Mathematics, Algebraic number, Topological entropy, Exponential function, Arithmetic zeta function, Discrete mathematics, [PHYS]Physics [physics], [MATH]Mathematics [math], Nonlinear Sciences - Chaotic Dynamics
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